The basic physical process used was 'secondary emission'; when the electron beam of the CRT hit the phosphor on the tube face, emits extra electrons, leaving a spot which is depleted of electrons. This leaves a 'well', a spot of electric charge. If the beam is then directed to a nearby spot, secondary electrons from that will fill the well.
This effect can be used to store data; if the well is left intact, that spot can be taken to represent 0, and if the well is filled, than can be 1.
To read the data out, the beam is briefly directed toward the original spot; depending on whether it held a well, or nothing, a tiny electrical signal is produced which can be picked up on a conductor plate placed close to the tube face, and amplified.
The charge wells tended to disappear fairly quickly, so the data had to be refreshed at a fairly high rate.